Supersymmetry breaking with fields, strings and branes

The first part of this review tries to provide a self-contained view of supersymmetry breaking from the bottom-up perspective. We thus describe (Formula presented) supersymmetry in four dimensions, the Standard Model and the MSSM, with emphasis on the “soft terms” that can link it to supergravity. The second part deals with the top-down perspective. It addresses, insofar as possible in a self-contained way, the basic setup provided by ten-dimensional strings and their links with supergravity, toroidal orbifolds, Scherk–Schwarz deformations and Calabi–Yau reductions, before focusing on a line of developments that is closely linked to our own research. Its key input is drawn from ten-dimensional non-tachyonic string models where supersymmetry is absent or non-linearly realized, and runaway “tadpole potentials” deform the ten-dimensional Minkowski vacua. We illustrate the perturbative stability of the resulting most symmetrical setups, which are the counterparts of circle reduction but involve internal intervals. We then turn to a discussion of fluxes in Calabi–Yau vacua and the KKLT setup, and conclude with some aspects of Cosmology, emphasizing some intriguing clues that the tadpole potentials can provide for the onset of inflation. The appendices collect some useful material on global and local (Formula presented) supersymmetry, in components and in superspace, on string vacuum amplitudes, and on convenient tools used to examine the fluctuations of non-supersymmetric string vacua.